Final answer:
To calculate the monthly payment for an installment loan, you use the loan payment formula with the principal amount, monthly interest rate, and total number of payments. For a $780 loan at 4.5% annual interest, paid monthly over 2 years, the monthly payment would come to approximately $33.65.
Step-by-step explanation:
Calculating Monthly Payments for an Installment Loan
To determine the monthly payment for an installment loan, you can use the loan payment formula:
PMT = P * (i / (1 - (1 + i)^(-n)))
where PMT is the monthly payment, P is the amount borrowed, i is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (time in years times the number of payments per year).
For the example provided, where $780 is financed at an annual interest rate of 4.5% with 12 payments per year over 2 years, we first calculate the monthly interest rate:
Monthly interest rate = Annual rate / 12
= 4.5% / 12
= 0.375% or 0.00375 in decimal
Then, calculate the total number of payments:
Total number of payments = Number of payments per year * Time in years
= 12 * 2
= 24 payments
Finally, we apply these values to the loan payment formula:
PMT = $780 * (0.00375 / (1 - (1 + 0.00375)^(-24)))
PMT = $780 * (0.00375 / (1 - (1.00375)^(-24)))
PMT = $780 * 0.043143534
PMT = $33.65 (rounded to two decimal places)
The monthly payment would be approximately $33.65.